The expression 30b -6c, when factorised is; 6(5b -c).
Factorization of ExpressionsThe factorisation of the given expression can be done by determining the common factor and hence; we have;
30b - 6c6(5b -c)Read more on factorisation:
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Two sides of a triangle have the following measures Find the range of possible measures for the third side 19 and 25
Answer should be
__< x <__
Answer:
The range of possible values for third side is:
[tex]44>x>6[/tex]
Step-by-step explanation:
Given side lengths are:
19 and 25
Let x be the third side
Then according to the triangle in equality theorem that sum of two sides has to be greater than third side,
The inequalities will be:
[tex]19+25>x\\25+x>19\\19+x>25[/tex]
We have to solve these inequalities to find the range
So,
[tex]19+25> x => 44>x\\25+x>19 => x >19-25 => x>-6\\19+x>25 => x> 25-19 => x>6[/tex]
We have to exclude the solution with negative value because the length of a triangle cannot be negative so from the other two inequalities x has to be less than 44 and greater than 6
Hence,
The range of possible values for third side is:
[tex]44>x>6[/tex]
Assume that the duration of human pregnancies can be described by a Normal distribution with mean 278 days and standard deviation 12 days. About 15% of babies are born prematurely. What is the length of a pregnancy that is the cutoff between being born prematurely and not being born prematurely?
Answer:
X = 262 days
Step-by-step explanation:
For Normal Distribution N( 0,1) we have z table and we can find z score for value of 15 % or 0,15. As 0,15 is not in the table we extrapolate then
0,1492 ⇒ 1,4
0,1515 ⇒ 1,3 0,15 ⇒ x 0,1515 - 0,15 = 0,0015
Δ = 0,0023 ⇒ 0,1
By rule of three
If 0,0023 ⇒ 0,1
0,0015 ⇒ x
x = 0,0652
Therefore the value between 1,3 and 1,4 is:
1,4 - 0,0652
z (score ) = 1,3348 and as we are looking for values below the mean ( that is at the left of the bell shape curve we need to change the value to a negative one z = - 1,3348
Now when N ( 278 , 12 ) is normalized to N ( 0 , 1)
z( score ) = ( X - μ ) / σ
- 1,3348 * 12 = X - 278
X = 278 - 16,0176
X = 278 - 16
X = 262 days
solve the following equation. 2/3 x + 6 = 1/2x + 1/4x
A. 6
B. 72
C. 14 2/5
D. 2
QUESTION:
Solve the following equation 2/3 x + 6 = 1/2 x + 1/4x
ANSWER:
In all choices the correct answer is B [tex]\blue{\boxed{72}}[/tex]
STEP-BY-STEP EXPLANATION:
[tex]\blue{\boxed{Note:}}[/tex] Since x is on the right side of the equation, switch the sides so it is on the left side of the equation
[tex] \frac{1}{2} x + \frac{1}{4} x = \frac{2}{3} x + 6[/tex]
First, Simply each term
Combine [tex]{\frac{1}{2}}[/tex], [tex]{\frac{1}{4}}[/tex] to x
[tex] \frac{x}{2} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] To write [tex]{\frac{x}{2}}[/tex] as a fraction with a common denominator, multiply by [tex]{\frac{2}{2}}[/tex]
[tex] \frac{x}{2} \times \frac{2}{2} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
Second, Write each expression with a common denominator of 4, by multiplying each by appropriate factor of 1
Multiply [tex]{\frac{x}{2}}[/tex] and [tex]{\frac{2}{2}}[/tex]
[tex] \frac{x \times 2}{2 \times 2} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
Multiply 2 and 2
[tex] \frac{x \times 2}{4} + \frac{x}{4} = \frac{2}{3} x + 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Combine the numerators over the common denominator
[tex] \frac{x \times 2 + x}{4} = \frac{2}{3} x + 6[/tex]
Third, Simplify the numerator
Move 2 to the left of x
[tex] \frac{2 \times x + x}{4} = \frac{2}{3} x + 6[/tex]
Add 2x and x
[tex] \frac{3x}{4} = \frac{2}{3} x + 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Combine [tex]{\frac{2}{3}}[/tex] and x
[tex] \frac{3x}{4} = \frac{2x}{3} + 6[/tex]
Fourth, Move all terms containing x to the left side of the equation
Subtract [tex]{\frac{2x}{3}}[/tex] from both sides of the equation
[tex] \frac{3x}{4} - \frac{2x}{3} = 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] To write [tex]{\frac{3x}{4}}[/tex] as a fraction with a common denominator, multiply by [tex]{\frac{3}{3}}[/tex]
[tex] \frac{3x}{4} \times \frac{3}{3} - \frac{2x}{3} = 6[/tex]
[tex]\blue{\boxed{Note Again:}}[/tex] To write [tex]{\frac{-2x}{3}}[/tex] as a fraction with a common denominator, multiply by [tex]{\frac{4}{4}}[/tex]
[tex] \frac{3x}{4} \times \frac{3}{3} - \frac{2x}{3} \times \frac{4}{4} = 6[/tex]
Fifth, Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1
Multiply [tex]{\frac{3x}{4}}[/tex] and [tex]{\frac{3}{3}}[/tex]
[tex] \frac{3x \times 3}{4 \times 3} - \frac{2x}{3} \times \frac{4}{4} = 6[/tex]
Multiply 4 and 3
[tex] \frac{3x \times 3}{12} - \frac{2x}{3} \times \frac{4}{4} = 6[/tex]
Multiply [tex]{\frac{2x}{3}}[/tex] and [tex]{\frac{4}{4}}[/tex]
[tex] \frac{3x \times 3}{12} - \frac{2x \times 4}{3 \times 4} = 6[/tex]
Multiply 3 and 4
[tex] \frac{3x \times 3}{12} - \frac{2x \times 4}{12} = 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Combine the numerators over the common denominator
[tex] \frac{3x \times 3 - 2x \times 4}{12} = 6[/tex]
Sixth, Simplify the numerator
Factor x out of 3x ×3 - 2x × 4
[tex] \frac{x(3 \times 3 - 2 \times 4)}{12} = 6[/tex]
Multiply 3 by 3
[tex] \frac{x(9 - 2 \times 4)}{12} = 6[/tex]
Multiply - 2 by 4
[tex] \frac{x(9 - 8)}{12} = 6[/tex]
Subtract 8 from 9
[tex] \frac{x \times 1}{12} = 6[/tex]
Multiply x by 1
[tex] \frac{x}{12} = 6[/tex]
[tex]\blue{\boxed{Note:}}[/tex] Multiply both sides of the equation by 12
[tex]12 \times \frac{x}{12} = 12 \times 6[/tex]
Seventh, Simplify both sides of the equation and cancel the common factor of 12
Cancel the common factor
[tex]12 \times \frac{x}{12} = 12 \times 6[/tex]
Rewrite the expression
[tex]x = 12 \times 6[/tex]
Lastly, Multiply 12 by 6
[tex]\blue{\boxed{ x = 72}}[/tex]
hope it's helps
Find the equation of the line passing through the point (-10, 3) that is PARALLEL to the line 5x+2y = 12
Answer:
[tex]y=-\frac{5}{2} x-22[/tex]
Step-by-step explanation:
Helpppppppp meeeeeeeeeeee
Catherina conducted a survey of four school cafeterias to find the number of students who like burgers for lunch. The results of her survey are recorded in the table below:
School Cafeteria Survey
School Total Number of Students
in the Cafeteria Number of Students
Who Like Burgers
A 35 15
B 42 13
C 21 8
D 41 16
Which school has the greatest percentage of students who like burgers for lunch?
School A
School B
School C
School D
Answer:
The answer is School A
Step by step explanation:
Answer:
a is your answer
Step-by-step explanation:
Can somebody help me with this??????
Answer:
Step-by-step explanation:
There needs to be a question to answer, that only the graph and the explanation.
The ________________ of -6 = 6 because it is 6 units from zero on the number line.
What's equivalent to 2x+3x+8-3x-2? Options arte 2x+6, 2x+10, 5x-3x+6, 5x-3x+10 Select all that are equivalent.
Answer:
2x+6, 5x-3x+6
Step-by-step explanation:
Please help!! I suck at math Help ASAP
scientists are studying the temperature on a distant planet. they find that the surface temperature at one location is 45° celsius. they also finf that the temperature decreases by 5° celsius for each kilometer you go up fron the surface. let T represent the temperature (in celsius) anf let H be the height above the surface (in kilometers)
Answer:
T=45-5H
Step-by-step explanation:
the equation shows direct variation
[tex]y = x - 7[/tex]
true or false ?
Answer: false.
Step-by-step explanation:
A direct variation equation is an equation where one fo the variable is equal to a constant times the other variable, we can write a general direct variation equation as:
y = k*x
Notice that the y-intercept is equal to zero in this type of equations.
Where y and x are the variables, and k is the constant.
In this case, we have the equation:
y = x - 7
Notice that in this equation we have a y-intercept equal to -7, which is different than zero.
Then the equation does not show direct variation, which means that the statement is false.
PLEASE HELP If the perimeter below is 70 units which equation is true?
Answer:
A
Step-by-step explanation:
25x means 25 times x
You burn 20 calories per minute biking for x minutes and 10 calories per minute walking for y
minutes. You spend a total of 80 minutes biking and walking and burn 1140 calories.
a. Write a system of equations to determine how much time you spend on each exercise.
b. How many minutes did you spend biking?
Answer:
Step-by-step explanation:
1140 divided by 10
Select all of the fractions that are equivalent to -2/3 –3/-2 -3/2 2/-2 2/-3 2/3 -2/-3 Please hurry and help I really need it
Answer:
2/-3
Step-by-step explanation:
Hope this helped. And I know that you can choose more than one, but I'm pretty sure this is the only one that's equivalent to -2/3
2) 19% of 72 is approximately what?
Answer:
Its 13.68
Step-by-step explanation:
just multiply 72 by 0.19
Think back to the verbal representations of math signs. "Of" means multiplication, so:
19% × 72 = 13.68
13.68 ≈ 13.7
(I'm not sure where you need to round, so round accordingly)
Find the coordinates of a point in Quadrant 3 that makes the following triangles congruent. Triangle GHJ: G(1,−6), H(2,−5), J(2,1) Triangle NOP: N(−6,1), O(−5,2)
Answer:
(-6, -5)Step-by-step explanation:
Plot the points first:
Triangle GHJ: G(1,−6), H(2,−5), J(2,1) Triangle NOP: N(−6,1), O(−5,2)Missing Point P is in quadrant 3and its coordinates are (-6, -5) as per symmetry with triangle GHJ.
The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R′(x)=(x+1)ln(x+1)R ′ (x)=(x+1)ln(x+1). Find the total revenue from the sale of the first 12 calculators. (Hint: In this exercise, it simplifies matters to write an antiderivative of x+1 as (x+8)2/2(x+8) 2 /2 rather than x2/2+x.)x 2 /2+x.)
Answer:
Total revenue = [tex]\frac{169}{2}\ln(13)-\frac{169}{4}[/tex] dollars
Step-by-step explanation:
[tex]R'(x)=(x+1)\ln(x+1)[/tex]
Integrate with respect to [tex]x[/tex].
[tex]R(x)=[/tex] ∫[tex](x+1)\ln(x+1)[/tex] dx
Take [tex]x+1=u[/tex]
Differentiate with respect to [tex]x[/tex]
[tex]dx=du[/tex]
So,
[tex]R(x)=[/tex] ∫[tex]u\ln(u)\,du[/tex]
Use integration by parts: ∫f g dx = f∫ g dx-∫(∫g dx)f' dx
Therefore,
[tex]R(x)=[/tex] [tex]\frac{u^2}{2}\ln(u)[/tex] [tex]-[/tex] ∫[tex]\frac{u^2}{2}\frac{1}{u}\,du[/tex]
= [tex]\frac{u^2}{2}\ln(u)[/tex] [tex]-[/tex] ∫[tex]\frac{u}{2}\,du[/tex]
Put [tex]u=x+1[/tex]
[tex]R(x)= \frac{(x+1)^2}{2}\ln(x+1)-\frac{(x+1)^2}{4}[/tex]
To find total revenue from the sale of the first 12 calculators, put [tex]x=12[/tex]
[tex]R(x)= \frac{(12+1)^2}{2}\ln(12+1)-\frac{(12+1)^2}{4}\\\\= \frac{(13)^2}{2}\ln(13)-\frac{(13)^2}{4}\\\\=\frac{169}{2}\ln(13)-\frac{169}{4}[/tex]
Total revenue = [tex]\frac{169}{2}\ln(13)-\frac{169}{4}[/tex] dollars
Mr. Kole has 30 students in his class. He has twice as many girls as boys. What is the ratio of boys to total students?
1:3
1:2
2:3
2:1
Answer:
1:3
Step-by-step explanation:
First, you need to make a system of equations for the situation.
Let G represent the number of girls and B represent the number of boys.
Since there are twice as many girls as boys,
G = 2B
There are a total of 30 students in class so,
G + B = 30
or
G + B = TOTAL
In order to find the ratio of BOYS to the TOTAL STUDENTS,
you plug in B values that make up G.
(2B ) + B = TOTAL
3B = TOTAL
B = TOTAL / 3 or (1/3) TOTAL
Since B is one third of the total number of students, the ratio is 1:3.
Answer:
1:3
Step-by-step explanation:
First, you need to make a system of equations for the situation.
Let G represent the number of girls and B represent the number of boys.
Since there are twice as many girls as boys,
G = 2B
There are a total of 30 students in class so,
G + B = 30
or
G + B = TOTAL
In order to find the ratio of BOYS to the TOTAL STUDENTS,
you plug in B values that make up G.
(2B ) + B = TOTAL
3B = TOTAL
B = TOTAL / 3 or (1/3) TOTAL
Since B is one third of the total number of students, the ratio is 1:3.
Hi! please help me the blue line is what I have to find and please show your work
Answer:
x = 2m
Step-by-step explanation:
2m−5−x+19=14
Step 1: Add -2m to both sides.
2m−x+14+−2m=14+−2m
−x+14=−2m+14
Step 2: Add -14 to both sides.
−x+14+−14=−2m+14+−14
−x=−2m
Step 3: Divide both sides by -1.
−x /−1 = −2m /−1
x = 2m
Evaluate (3−1)³+7(6)−5²
Answer:
25
Step-by-step explanation:
Answer:
The answer is 25.
Step-by-step explanation:
Solve the system of equations by using elimination.
-8a+7b=-69
-3a-3b=-9
ANSWERS;
A)5,-6
B)-6,5
C)6-3
D)-36
Answer: a=6, b=-3 (choice c) Let me know if you need step by step.
Step-by-step explanation:
Pls help me on this question
Answer:
yes
Step-by-step explanation:
If you was to do the vertical line test only one point would have one output so it would be a function
Answer:
Yes
Step-by-step explanation:
every x value has only one y value. You can also do the vertical line test. with a ruler and if there is only on point on the ruler at all time, it is a function
Combine the like terms to create an equivalent expression 4p+6-3
Answer:
-3/4
Step-by-step explanation:
4p+6-3=0
4p+3=0
4p=-3
p= -3/4
Please help
Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?
A.)The amount of gas you use. B.)70. C.)The amount of hours you drive. D.)The distance you drive
Answer:
The amount of hours you drive.
Step-by-step explanation:
I did the test.
Answer:
C.)The amount of hours you drive.
Step-by-step explanation:
Given parallelogram PQRS with P(-4,-2), Q(-2,3), R(4,3) and S(2,-2). Find the perimeter of PQRS.
Answer: it’s C
Step-by-step explanation:
The required perimeter of the parallelogram PQRS is 12 + 2√29. Option D is correct.
Given that,
parallelogram PQRS with P(-4,-2), Q(-2,3), R(4,3) and S(2,-2).
Perimeter is the measure of the figure on its circumference.
Here,
Length of PQ = √[(-2 + 4)² + (3+2)²]
= √[4 + 25]
= √29
Length of QR = √[(4+2)² + (3-3)²]
= √36
= 6
Now the perimeter of the parallelogram = 2 PQ + 2 QR
= 2√29 + 2 * 6
=12 + 2√29
Thus, the required perimeter of the parallelogram PQRS is 12 + 2√29. Option D is correct.
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Anyone please help I just need the solution!!
Answer:
x < -5Step-by-step explanation:
[tex]x + 9 < 4[/tex]
Subtract 9 from both sides
[tex]x + 9 - 9 < 4 - 9[/tex]
Simplify
[tex]x < - 5[/tex]
Consider the following binomial experiment: A newspaper publisher claims that 52% of the people in a certain community read his newspaper. Doubting the assertion, a competitor randomly surveys 289 people in the community. Find the standard deviation of this experiment, if the newspaper publisher's claim is correct.
a) 8.1932
b) 8.3932
c) 8.4932
d) 8.6932
e) 8.5932
f) None of the above.
Answer:
[tex]SD = 8.4932[/tex]
Step-by-step explanation:
Given
[tex]Sample\ Size (n) = 289[/tex]
[tex]proportion, p= 52\%[/tex]
Required
Determine the standard deviation (SD)
The standard deviation of a binomial distribution is calculated as thus:
[tex]SD = \sqrt{np(1-p)}[/tex]
Substitute values for n and p
[tex]SD = \sqrt{289 * 52\% * (1-52\%)}[/tex]
Convert to decimals
[tex]SD = \sqrt{289 * 0.52 * (1-0.52)}[/tex]
[tex]SD = \sqrt{289 * 0.52 * 0.48}[/tex]
[tex]SD = \sqrt{72.1344}[/tex]
[tex]SD = 8.49319727782[/tex]
[tex]SD = 8.4932[/tex] --- approximated
Hence, the calculated standard deviation is approximately 8.4932
1) Identify the x- and y-intercepts of the functions below. (Graphs shown below)
2) Algebraically, find the zero(s) and y-intercept of each function:
- f(x)=3x^2+5x-2, g(x)=2x^4-20x^2+18
9. Which list shows these numbers in order from least to greatest?
Answer:
It the first one
Step-by-step explanation:
